Question: Find the domain of the function
\[g(x) = \frac{x^3 + 11x - 2}{|x - 3| + |x + 1|}.\]
Solution: The expression is defined as long as the denominator $|x - 3| + |x + 1|$ is not equal to 0.  Since the absolute value function is always non-negative, the only way that $|x - 3| + |x + 1| = 0$ is if both $|x - 3|$ and $|x + 1|$ are equal to 0.  In turn, this occurs if and only if $x = 3$ and $x = -1$.  Clearly, $x$ cannot be both 3 and $-1$ at the same time, so the denominator is always non-zero.  Therefore, the domain of the function is $\boxed{(-\infty,\infty)}.$